You should build a frame which should have a max of 24 inches between planks and preferably attach this to a straight wall. Use screws around the outside and something like "no nails" for everything in the middle. No part of the MDF should be untreated as this will cause the wood to work too much. If there is a possibility of damp (eg if its attached to an outside wall) you should insulate the back of the screen protecting it from damp. If its well build it should remain perfectly straight.
In the USA, white blackout cloth works well. Bright white cloth with vinyl backing to block out light (originally designed for windows behind drapes or to be sewn to the back of drapery to block out sun light and give more privacy). It's cheap ($4-5/yd USD for 54" width) and easily found in local fabric shop. In Europe, I'm not sure but you may ask your local fabric or art stores.
Some people use drywall or sheetrock to paint/make their screen as it does not warp like plywood, thin MDF, or formica.
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